Fractional Heat Conduction in an Infinite Medium with a Spherical Inclusion

The problem of fractional heat conduction in a composite medium consisting of a spherical inclusion ) 0 ( R r   and a matrix ) (    r R being in perfect thermal contact at R r  is considered. The heat conduction in each region is described by the time-fractional heat conduction equation with the Caputo derivative of fractional order 2 0   and , 2 0    respectively. The Laplace transform with respect to time is used. The approximate solution valid for small values of time is obtained in terms of the Mittag-Leffler, Wright, and Mainardi functions.